Properties

 Label 4560.bd Number of curves $2$ Conductor $4560$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

Elliptic curves in class 4560.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.bd1 4560bb2 $$[0, 1, 0, -6360, -197100]$$ $$6947097508441/10687500$$ $$43776000000$$ $$$$ $$4608$$ $$0.94121$$
4560.bd2 4560bb1 $$[0, 1, 0, -280, -4972]$$ $$-594823321/2166000$$ $$-8871936000$$ $$$$ $$2304$$ $$0.59464$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 4560.bd have rank $$0$$.

Complex multiplication

The elliptic curves in class 4560.bd do not have complex multiplication.

Modular form4560.2.a.bd

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + 2 q^{7} + q^{9} + 2 q^{11} + q^{15} - 2 q^{17} - q^{19} + O(q^{20})$$ Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 